So, what is the added value of our setup with respect to existing ones, in terms of representation of real-world phenomena?
To provide an answer through an example, let us stick to the co-authorship model of Example REF .
Imagine that agents \(i\) , \(j\)  and \(k\)  set up a project \(p \)  together, so that \(|n( p )|=3\) . This could be represented in the original co-authorship model of [1]}, that allows only for couples, by saying that \(i\)  is linked to \(j\)  and \(k\) , and \(j\)  and \(k\)  are also linked together.
We observe that the link between \(i\)  and \(j\)  would have a negative externality on each neighbor of these agents, including \(k\) .
However, in the general setup and in reality, the fact that \(i\)  and \(j\)  are in a three-agent collaboration has a positive externality on the third agent \(k\) , and a negative externality on the others.
Formally, this could be done in the original network formation model by specifying, for each link between two agents, and for any other agent, the sign of the externality of that link on the third agent.
It is clear that this would seriously complicate the notation, and that only a more general framework such as the one we use can overcome such difficulties.
